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Deflationary truth and pathologies. (English) Zbl 1197.03054

Summary: By a classical result of Kotlarski, Krajewski and Lachlan, pathological satisfaction classes can be constructed for countable, recursively saturated models of Peano arithmetic. In this paper we consider the question of whether the pathology can be eliminated; we ask in effect what generalities involving the notion of truth can be obtained in a deflationary truth theory (a theory of truth which is conservative over its base). It is shown that the answer depends on the notion of pathology we adopt. It turns out, in particular, that a certain natural closure condition imposed on a satisfaction class – namely, closure of truth under sentential proofs – generates a nonconservative extension of a syntactic base theory (Peano arithmetic).

MSC:

03H15 Nonstandard models of arithmetic
03A05 Philosophical and critical aspects of logic and foundations
03F30 First-order arithmetic and fragments

References:

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